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# Previous Puzzles of the Month + Solutions

July-September 2009, Puzzle nr 122
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Puzzle # 122 Difficulty level: , general math knowledge.

 Radiolarian's shell    A radiolarian is a single-celled protozoa living in all the world’s ocean. Most of them have a spherical shell that survives as a fossil. We discovered a radiolarian with a perfect spherical shell having 384 circular holes arranged in a triangular pattern. Most of the holes are surrounded by six other holes, but some are surrounded by ONLY five.   The question is: how many holes have only five neighbors? Give a geometrical proof and explain steps and reasoning Keywords: polyhedron, sphere, Euler's formula. Related puzzles: - Euler's Graeco-Latin squares. - Radiolare sferico Alcuni radiolari, animali acquatici unicellulari, hanno uno scheletro/guscio poliedrico. Ne abbiamo trovato uno che possiede un guscio perfettamente sferico con 384 buchi circolari disposti sulla superficie in modo triangolare. Ognuno dei buchi è circondato da 6 altri, tranne alcuni che sono circondati da soli 5 altri buchi. La domanda è: quanti sono i buchi circolari sulla sfera circondati da soli 5 altri buchi? Parole chiave: poliedro. Suggerisci un'altra soluzione Chiudi - Radiolaire sphérique Certains radiolaires, organismes aquatiques unicellulaires, possèdent des squelettes / capsules en forme de polyèdre. Nous en avons trouvé un avec un squelette parfaitement sphérique percé de 384 trous circulaires, disposés en surface de façon triangulaire. Chaque trou est entouré de 6 autres trous, sauf quelques-uns qui sont entourés de 5 trous seulement. Question: combien y a-t-il de trous circulaires sur la sphère à être entourés de 5 trous seulement? Mots clés: polyèdre. Propose une autre solution Fermer Source of the puzzle: BrainTrainer, issue #28. © G. Sarcone. You cannot reproduce any part of this page without prior written permission.

 More Math Facts behind the puzzle Leonhard Euler (1707 - 1783), icosahedron and polyhedron formula The stamp issued in 1983 by the German Democratic Republic honoured Euler on the occasion of the 200th anniversary of his death and shows an icosahedron, one of the five Platonic solids, along with the Euler's polyhedron formula. In 1988, mathematicians worldwide were asked to vote for their favourite theorems. Euler's polyhedron formula finished second, Euclid's theorem "There are exactly five Platonic solids" finished 4th.

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